# Efficiency Puzzle — Summary of Attenuation Results

How much does each channel explain the aging → innovation disconnect?

| Specification | DV | Z_1 coef | Z_1 sig | Attenuation % | R² | N |
|:-------------|:---|:---------|:--------|:--------------|:---|:--|
| Baseline: Z → patents_pm | patents_per_million | -2239.3903 | * | — | 0.1740 | 1163 |
| Baseline: Z → rd_efficiency | rd_efficiency | -0.3834 |  | — | 0.1009 | 693 |
| + Health expenditure → patents_pm | patents_per_million | -1038.3279 |  | 53.6% | 0.1231 | 854 |
| + Health expenditure → rd_efficiency | rd_efficiency | 3.9963 |  | 1142.3% | -0.0713 | 586 |
| + Manufacturing VA → patents_pm | patents_per_million | -1860.4015 | * | 16.9% | 0.1650 | 1080 |
| + Manufacturing VA → rd_efficiency | rd_efficiency | -0.4999 |  | -30.4% | 0.0618 | 667 |
| + Human capital → patents_pm | patents_per_million | -2619.0924 | * | -17.0% | 0.1847 | 1021 |
| + Human capital → rd_efficiency | rd_efficiency | -2.2140 |  | -477.5% | 0.1589 | 619 |

## Interpretation

Attenuation % measures how much the Z_1 coefficient shrinks when the channel 
variable is added as a control. Higher attenuation = more of the demographic 
effect on innovation is mediated through that channel.
